Linear Systems word problem

Question

How many pounds of peanuts at $2.50 per pound and cashews at $3.60 per pound should be used to obtain 100 pounds of mixed nuts valued at $316.00?

Answer 1

Let p = the number of pounds of peanuts.

Let c = the number of pounds of cashews.

 

p + c = 100 (eq1)

2.5p + 3.6c = 316 (eq2)

 

Solve eq1 for either p or c:

p = 100 - c

 

Substitute into eq2 and solve for the other variable:

2.5(100 - c) + 3.6c = 316

250 - 2.5c + 3.6c = 316

1.1c = 66

c = 60

 

Substitute into eq1:

p = 100 - 60

p = 40.

 

You will need 40 pounds of peanuts and 60 pounds of cashews.

Answer 2

Let there be x pound of peanuts and 100-x pounds of cashews.

2.5x+3.6(100-x) = 316

2.5x+360-3.6x=316

-1.1x=-44

x=40

100-x =100-40=60